In vane cell pumps of the type cited, the pressure fluid delivered by the pump is applied to (each of) the one or more vanes in the sub-vane region, in order to ensure that even in the lower rotational speed range, such as for example when the pump is started up, the vane(s) is/are pressed outwards towards a cam structure surrounding the rotor, in order to fluidically separate the delivery cells of the pump from each other. Supplying the sub-vane region is associated with a reduction in the effectiveness of the pump.